1. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines 8-5 Law of Sines and Law of Cosines Holt GeometryHolt McDougal Geometry

2. 8-5 Law of Sines and Law of Cosines Warm Up 1. What is the third angle measure in a triangle with angles measuring 65° and 43°? Find each value. Round trigonometric ratios to the nearest hundredth and angle measures to the nearest degree. 2. sin 73°3. cos 18°4. tan 82° 5. sin -1 (0.34)6. cos -1 (0.63)7. tan -1 (2.75)

3. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. A. tan 103° B. cos 165°C. sin 93°

4. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Use the law of sines in a non-right triangle in you are provided with the measurements of an angle opposite a side.

5. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. FG

6. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. NP

7. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mQmQ

8. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mLmL

9. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mXmX

10. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. AC

11. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Solve each triangle. f = 9.1, r = 20.1, m R = 107 ᵒ

12. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Solve each triangle. mR = 71 ᵒ, m F = 41 ᵒ, r = 7.4

13. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Solve each triangle. m R = 34 ᵒ, f = 9.1, r = 27

14. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Solve each triangle. m F = 25 ᵒ, mD = 52 ᵒ, r = 15.6

15. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Solve each triangle. d = 30, r = 9.5, m D = 107 ᵒ

16. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines LAW OF COSINES Day 2

17. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Use the law of cosines if are NOT provided with a side opposite an angle.

18. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. XZ

19. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mTmT

20. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mTmT

21. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. DE

22. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mKmK Sbtract 325 both sides.

23. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mKmK

24. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. YZ

25. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mRmR

26. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mRmR

27. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines A sailing club has planned a triangular racecourse, as shown in the diagram. How long is the leg of the race along BC? How many degrees must competitors turn at point C? Round the length to the nearest tenth and the angle measure to the nearest degree.

28. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines What if…? Another engineer suggested using a cable attached from the top of the tower to a point 31 m from the base. How long would this cable be, and what angle would it make with the ground? Round the length to the nearest tenth and the angle measure to the nearest degree. 31 m

29. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Round lengths to the nearest tenth and angle measures to the nearest degree. 1. mB = 20°, mC = 31° and b = 210. Find a. 2. a = 16, b = 10, and mC = 110°. Find c. 3. a = 20, b = 15, and c = 8.3. Find mA.

30. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines 4. An observer in tower A sees a fire 1554 ft away at an angle of depression of 28°. To the nearest foot, how far is the fire from an observer in tower B? To the nearest degree, what is the angle of depression to the fire from tower B?